Raman E 1 and E 1 + Δ1 resonances in a system of unstrained germanium quantum dots

The positions and shapes of the Raman E ₁ and E ₁ + Δ₁ resonances of optical phonons are studied as functions of the size of unstrained germanium quantum dots. The quantum dots are grown by molecular-beam epitaxy in GaAs/ZnSe/Ge/ZnSe structures on GaAs(111) wafers. The positions of the E ₁ and E ₁ + Δ₁ resonances are found to shift by at most 0.3 eV. This shift is shown to be well described in terms of a cylindrical model using the quantization of the spectrum of bulk electron-hole states in germanium that form an exciton in a two-dimensional critical point. The fact that the peaks of the E ₁ and E ₁ + Δ₁ resonances appear separately has been detected for the first time, and it is related to the transformation of the interband density of states into a delta function because of spectrum quantization. An increase in the resonance amplitudes in quantum dots as compared to the bulk case is related to the degeneracy multiplicity of the exciton state in the (111) direction.